Abstract

We consider the application of the Bragg–Pippard (BP) equations for form birefringence to a tilted-columnar biaxial thin film with columns of index n _c and voids of known index n _v. In such a situation the three forward BP equations that express the principal refractive indices n ₁, n ₂, and n ₃ as functions of n _c, n _v, the packing fraction p _c, and the depolarization factors L ₁, L ₂, and L ₃ can be inverted. The procedure described for adding dispersion to the principal indices involves entry to the BP model via the inverted equations, modification of n _c to allow for dispersion, and then exit from the model via the forward BP equations. We discuss the introduction of composite columns to the model to allow for angular dependence of n _c and the selection of suitable dispersion functions for bulk tantalum oxide, titanium oxide, and zirconium oxide. Theory and experiment both show that the dispersion of the normal-incidence birefringence Δn of the thin films is several times larger than the dispersion of the individual principal refractive indices.

© 2001 Optical Society of America

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